{"product_id":"elementary-operator-theory-paperback","title":"Elementary Operator Theory - Paperback","description":"\u003cp\u003eby \u003cb\u003eMarat V. Markin\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe book is intended as a text for a one-semester graduate course in operator theory to be taught \"from scratch'', not as a sequel to a functional analysis course, with the basics of the spectral theory of linear operators taking the center stage. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eThe book consists of \u003cem\u003esix chapters\u003c\/em\u003e and \u003cem\u003eappendix, \u003c\/em\u003e with the material flowing from the fundamentals of abstract spaces (metric, vector, normed vector, and inner product), the \u003cem\u003eBanach Fixed-Point Theorem\u003c\/em\u003e and its applications, such as \u003cem\u003ePicard's Existence and Uniqueness Theorem\u003c\/em\u003e, through the basics of linear operators, two of the three fundamental principles (the \u003cem\u003eUniform Boundedness Principle\u003c\/em\u003e and the \u003cem\u003eOpen Mapping Theorem\u003c\/em\u003e and its equivalents: the\u003cem\u003e Inverse Mapping\u003c\/em\u003e and \u003cem\u003eClosed Graph Theorems\u003c\/em\u003e), to the elements of the spectral theory, including \u003cem\u003eGelfand's Spectral Radius Theorem\u003c\/em\u003e and the \u003cem\u003eSpectral Theorem for Compact Self-Adjoint Operators\u003c\/em\u003e, and its applications, such as the celebrated \u003cem\u003eLyapunov Stability Theorem\u003c\/em\u003e. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eConceived as a text to be used in a classroom, the book constantly calls for the student's actively mastering the knowledge of the subject matter. There are problems at the end of each chapter, starting with Chapter 2 and totaling at 150. Many important statements are given as problems and frequently referred to in the main body. There are also 432 Exercises throughout the text, including Chapter 1 and the Appendix, which require of the student to prove or verify a statement or an example, fill in certain details in a proof, or provide an intermediate step or a counterexample. They are also an inherent part of the material. More difficult problems are marked with an asterisk, many problems and exercises are supplied with \"existential'' hints. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eThe book is generous on Examples and contains numerous Remarks accompanying definitions, examples, and statements to discuss certain subtleties, raise questions on whether the converse assertions are true, whenever appropriate, or whether the conditions are essential. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eWith carefully chosen material, proper attention given to applications, and plenty of examples, problems, and exercises, this well-designed text is ideal for a one-semester Master's level graduate course in operator theory with emphasis on spectral theory for students majoring in mathematics, physics, computer science, and engineering. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e\u003cstrong\u003e\u003c\/strong\u003e \u003cp\u003e\u003cstrong\u003eContents\u003cbr\u003e\u003c\/strong\u003ePreface \u003cstrong\u003e\u003cbr\u003e\u003c\/strong\u003ePreliminaries\u003cbr\u003eMetric Spaces\u003cbr\u003eVector Spaces, Normed Vector Spaces, and Banach Spaces\u003cbr\u003eLinear Operators\u003cbr\u003eElements of Spectral Theory in a Banach Space Setting\u003cbr\u003eElements of Spectral Theory in a Hilbert Space Setting\u003cbr\u003eAppendix: The Axiom of Choice and Equivalents \u003cbr\u003eBibliography\u003cbr\u003eIndex \u003c\/p\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003cstrong\u003eMarat V. Markin\u003c\/strong\u003e, California State University, Fresno, USA.\u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 425\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 1 x 9.3 x 6.7 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e April 06, 2020\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":51758631813408,"sku":"9783110600964","price":92.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0974\/9764\/5344\/files\/5efec9cc270333573479c1ac01de53ec.webp?v=1780131045","url":"https:\/\/ebocreations.com\/products\/elementary-operator-theory-paperback","provider":"The E-Book Oasis LLC","version":"1.0","type":"link"}